Problem $1.$ Derive an expression for the partition function Q$($T$,$ N$,$ V $)$ of

ideal homonuclear diatomic gas. Assume vibration and rotations to be in

the low$-$temperature and high$-$temperature limits$,$ respectively. Then compute the Helmholtz free energy A$($T$,$ N$,$ V $),$ entropy S$($T$,$ N$,$ V $),$ heat capacity

CV$($T$,$ N$,$ V $),$ chemical potential $($T$,$ N$,$ V $),$ and derive an equation of state.

The mass of a nucleous is m$.$ If you feel it is too hard for you, do the same

calculations for ideal monatomic gas.